facty/src/factorization/fermat.js

Integer Factorization Approaches with JavaScript

const { add, ceil, isSquare, number, pow, sqrt, smallerEq, subtract } = require('../utils/math');

/**
 * Fermat's Factorization Method
 * https://www.wikiwand.com/en/Fermat%27s_factorization_method
 * 
 * Since this method is based on the representation of an odd
 * integer as the difference of two squares, we limited to odd numbers.
 * 
 * @param {Number} n 
 */
const fermatsFactorizator = n => {
  for (let x = ceil(sqrt(n)); smallerEq(x, n); x = add(x, 1)) {
    const ySquared = subtract(pow(x, 2), n);

    if (isSquare(ySquared)) {
      const y = sqrt(ySquared);

      return [
        number(subtract(x, y)),
        number(add(x, y)),
      ];
    }
  }
};

fermatsFactorizator.oddOnly = true;

module.exports = fermatsFactorizator;